book-recommendations

[keen orbit]

tysm @tender cobalt

[remote sparrow]

yeah shifrin has lectures on youtube for his book too

[keen orbit]

this is nice , one can refer to the videos sometimes for some clarification

i see he is dedicated to teach this course

[remote sparrow]

durrett is free online, but it's kind of a learn through exercises kind of book

the problems have a reputation for being challenging

[north summit]

what about this one https://www.amazon.com/Probability-Theory-Courant-Lecture-Notes/dp/0821828525

silverman a friendly introduction to number theory

[remote sparrow]

no clue

[tender cobalt]

yeah

it's awesome

[stable flicker]

Hmm never really flipped through this one. Should be https://math.nyu.edu/~varadhan/limittheorems.html

https://mypage.cuhk.edu.cn/academics/wkshum/MAT3280ProbabilityTheory.html has comments on Varadhan, along with a very long list of textbooks. I have not seen Shum before, but would recommend Shiryaev if you can go through it slowly

[trail hemlock]

ts book is ahh 🥀🥀🥀

[remote sparrow]

what does this mean

[vital bane]

it means "ts book is ahh wilted_rose wilted_rose wilted_rose"

you are welcome, no need to thank me

[remote sparrow]

[uncut salmon]

Book solely on Galois Theory (with excercises)?

I already studied a bit of it in an algebra course, e.g. we covered the main theorem, so if the book is more advanced it's better.

Plz🤠

[desert crane]

Read op centre out of the ashes

[full cairn]

Galois Theory through Exercises has a pretty good selection of exercises with both hints and solutions. The exposition is not very comprehensive though, so you should combine it with another book

[uncut salmon]

Thanks that's really helpful💓

[remote sparrow]

https://www.amazon.com/Galois-Theory-David-Cox/dp/1118072057

[uncut salmon]

Thankss

[grave flume]

I am reading about Mobius function and came across Kronecker delta (δ), the Liouville function (λ), and the number of distinct (ω(n)) and total (Ω(n)) prime factors of n.
Can someone please suggest me a book where I can start with these from basics? Having some problems to solve would be a huge + as well.
Thanks

[cursive rivet]

<@&268886789983436800>

[static spoke]

any good websites or books to practice functions, but not advanced? topics such as: domain and range, asymptotes, rational functions, inverse and composite functions, transformations (translations, reflections, stretches)

[rich sun]

stewart's calculus, maybe

[remote sparrow]

@naive lava just curious, have you heard of A Course in Complex Analysis by saeed zakeri?

[naive lava]

I looked a bit trough it but i wanted a geometric view so i didn't look too much into it

[naive lava]

It's one of the recommended readings for my class

[remote sparrow]

isn't it pretty geometric though?

[naive lava]

it's more geometric than lang, conway or narasimhan but i think it was worse than ahlfors in that regard

also general content is represented in a very modern way

no reimann zeta too

[molten gulch]

What would you say is a good book for CA with geometric intuition? Ahlfors? Any other texts you've enjoyed?

[naive lava]

I am definitely not an expert on this but i can give you my prof's word(he works in riemann surfaces and shi), he prefers ahlfors over any book because he says it has a very good selection of topics so that you can go any way you want, and it's a cult classic, I'm also reading ahlfors atm and i'm quite enjoying it, ppl compare it to rudin but it's much much different, he actually takes time to convince you, explore some fun stuff, and it's joy to read tbh, zakeri is a new thing that goes somewhat into these stuff, but it has a different way of going trough the content, so idk much about it, wegert is nice to have, to see thing, but i don't think that'd be a good way to learn everything, and i heard palka is nice too, it's pretty much inspired by ahlfors so you'll find some nice geometry in it too

[molten gulch]

Thanks, I feel that the biggest issue I have with CA is the ability to easily visualize complex functions

With RA or calculus it's easy for me to associate a graph to a function, I don't feel comfortable doing that in C

[naive lava]

ahlfors really did that for me

just imagining mapping a complex plane to a complex plane

or visualizing riemann sphere for menemorphic(i can't spell) functions is a game changer

you might wanna check out wegert too it's really nice in that regard, or so i heard

[molten gulch]

I will do, thank you

I assume the prereq for both would be first few chapters of rudin equivalent levels of RA?

[vast jackal]

are programming textbooks worth it than lectures?

[molten gulch]

I use both, textbooks alongside attending lecture

[naive lava]

yeah more or less, for ahlfors def being familiar with epsilon delta is required, but you won't need actual definition of riemann integrals and whatot

he also goes over series/sequences/sequence of functions but briskly

(is that the right word?)

[molten gulch]

yeah that's correct

[gray gazelle]

What is an approachable book on Geometric Measure theory that is not the bible of the subject? I found that the "bible" is just a thick research manual, by the manual I'm talking about Ferder's book

[keen vale]

what book do you guys recommend to get into graph theory as a compsci major?

[gloomy spire]

What are some good books that talk about lattices, with a view towards lattice based cryptography? I've taken an algebra course before but nothing too crazy

[foggy quest]

Some chapters and appendices of this book: https://bookstore.ams.org/gsm-76. Like chapter 12 and appendices E through I

[timber holly]

https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/f471f7b7034fabe8bbba5507df7d307f_MIT6_042JF10_chap05.pdf

also once you get into that you should make a maze solver

you’ll be able to understand dfs and bfs and maze solvers teach a lot of stuff

I assume you use Java for your comp sci curriculum

I can lend you a maze to solve if so

[timber holly]

https://link.springer.com/book/10.1007/978-0-387-77993-5

youll be able to find some pdf online

[keen vale]

i use cpp, but thanks for the resources

[timber holly]

c++? I can make it work sure gimme a moment I think I have one somewhere

[gloomy spire]

danke danke

[gloomy spire]

turned out i already had it downloaded

[timber holly]

its the go to after all

more hands on approach https://us.artechhouse.com/Learning-and-Experiencing-Cryptography-with-CrypTool-and-SageMath-P2378.aspx

[grave flume]

Can soeone help here?

[vast jackal]

lecture makes me sleepy

like those online lectures

recorded ones

[vast jackal]

hey after i learn C will c++ be an easy going language for me?

I'm interested in kernel development/os development

[keen vale]

i'm not sure, from what i've heard, c++ is more difficult than c

[vast jackal]

from what I've heard too is that c++ is just a superset of C with tons of features and object oriented one

[sonic talon]

pretty much

though it's not a strict superset

c is kinda like the smaller core language, c++ is a never ending list of additions that people thought would be cool over the past 30 years or so

[still panther]

its not hard to write C++ if you can write C

but it's miles harder to know C++ than it is to know C, like not even in the same league

[vital bane]

Visual Complex Analysis by Tristan Needham

it has "visual" in the title

[timber holly]

ill link it here for others to find if they need it https://github.com/transparentdino/C-maze/tree/main

[merry sphinx]

besides the "obvious" visual complex analysis rec, maybe gamelin, i read around the first chapter and it seemed to have a lot of visual/geometrical stuff as well

[remote sparrow]

you could also read something that mostly represses geometric content like bak and newman in favor of a power series first approach

@naive lava actually have you heard of marshall's Complex Analysis? it's a power-series first approach

[naive lava]

Wait i must have a review of that book iirc

[naive lava]

https://mathoverflow.net/a/332408

Haven't checked it out myself yet

[remote sparrow]

this guy @silent @marble solar loves it

[naive lava]

But power series first is a trend in CA cos most results follow from that and the interest is differentiable functions which are analytic anyhow

[remote sparrow]

damn silent didn't work

@dapper root thinks marshall is good too

[naive lava]

I honestly don't know much about that book

Remmert was cool too

My end goal with CA is complex manifolds so I'm kinda focusing on books designed like that

[remote sparrow]

https://www.amazon.com/Complex-Analysis-Cambridge-Mathematical-Textbooks/dp/110713482X

only review i'm aware of is on amazon

[naive lava]

Check out the link i sent

[remote sparrow]

doesn't say much about the book tbh

all it says is that it's good

without going much into depth about how it treats CA

[naive lava]

Yeah but that's all i have

I'll drop by my profs office tomorrow i can ask for his opinion

[vast jackal]

damn but I'm going to the path of kernel/os development

[naive lava]

https://www.youtube.com/watch?v=tsG95Y-C14k& this pretty much sums up my entire opinion on cpp

very fun video too

[mossy flume]

cppcon videos are fun to watch

[still panther]

one of my favorite cppcon videos of all time

[molten gulch]

you need to put @silent at the beginning of the message

[vital bane]

this guy is kinda wacko @molten gulch

did that work?

[molten gulch]

nop sadly, it did ping us

[vital bane]

RIP

I guess silent means something else then

[molten gulch]

silent is useful in DM's to not ping the other members of a DM or GC

it also doesn't cause the channel to get highlighted due to it

but otherwise it doesn't suppress any pings inside the message

[vital bane]

hm I see

Look up Dissociative Identity Disorder

[hearty steppe]

Any recs for learning percolation theory?

[gray gazelle]

This might be better suited for the Physics server, of course it's allowed here, but you'd probably get better answers there

[dapper root]

How tf do you remember this

[tribal crow]

Sour Drop knows all 👁️

in regards to books and peoples’ preferences :p

[subtle violet]

i'm probably known as the guy who spent a year banging his head against grimmett and stirzaker

[molten gulch]

@fair fiber where the heck did you find a link to my server from- /genq

[trail hemlock]

https://notesfromkevinrvixie.org/2012/11/02/geometric-measure-theory-by-the-book-2/
this is the post i used to select a book, I ended up going with Measure Theory and Fine Properties of Functions

[slate wedge]

What textbooks do you guys recommend for calculus?

[green swan]

larson is decent, stewart is good, and spivak you shouldn't touch with a 30 foot pole unless you wanna be a pure math major

[gray gazelle]

Why else would you be asking about math in a math server unless you wanted to learn pure math

[green swan]

because there are other non pure math fields that require math?

[slate wedge]

I want to major in math😭 what makes spivaks different from Larson and Stewarts?

[mortal ore]

https://tenor.com/view/agh-quit-gif-498994852169174544

[green swan]

Larson and Stewart are more akin to what undergrad calc classes will teach you, aka, "here is a theorem, and here is how to use it. Here are some problems that require you to apply the theorems." Spivak practice problems are entirely proofs

[real marsh]

spivak is a good book

[green swan]

So while Larson or stewart will teach you how to use the Lagrange error bound to find the error of a Taylor approximation for example, spivak will have you prove why that works

[real marsh]

Spivak is a great book for going from 'math' in high school to actual math classes

[normal crystal]

99.99% of the server ignored

[real marsh]

everything except pure math is just stamp collecting

[gray gazelle]

They’d presumably ask in said server, though?

Like say they’re an engineer

Why go to a math server to look to learn engineering math

Instead of an engineering server

[vital bane]

math and engineering math aren't different, they're both math

Euler and Gauss were doing the so called "engineer" math they weren't writing rigorous proofs using ZFC

[upper estuary]

I'm halfway through Stewarts and I can vouch for it! There are plenty of both simple problems to practice specific techniques, and plenty of problems that you need to really get creative to solve.

I found some proofs a bit hard to follow but overall I'd say it's an amazing book

[tender cobalt]

frfr

[peak bronze]

Uhm, any good books on trig and coordinate geometry? something shortly coverable with good difficult problems;

Russians books are good but hard to get, and often have very hard to read in terms of text quality.

[vital bane]

Engineers don't say that either lol

that's just a meme

pi = e = 3

[stiff cave]

cosx = 1

u mean taylor series?

🤨

well thats mathematically valid and its not just in physics

in a situation where the limit approaches 0, sinx can be written as x

there are certain ways u should/shouldn't apply it but yeah

in a limit its valid

like i said above

f(x)=sinx
f(0)=0
f'(0)=/= 0
therefore sinx has only degree 1 at x=0, so u dont have to expand the taylor series further for when limit x->0

i know what ur trying to say but it doesnt apply to this situation

like pi=3

the joke is based on the fact that non-math majors have a very hand wavy approach to proofs

but taylor polynomials arent some pi=3 type shit

[stiff cave]

in a limit it is valid

i think ive said this 3 times

[vital bane]

Not in proofs, but when solving problems sin(x) = x is an application of Taylor's theorem, commonly called the small angle approximation, very useful for solving the simple harmonic oscillator, you get a linear ODE this way. If you don't employ this, you get a non-linear ODE and it's harder to analyze that system and use it and teach it to high school/undergraduate students

yea that's what they say, they say sin(x) is approximately x in a neighborhood of 0 \in R

Physicists don't care about mathematical rigor because they are not trying to study math, they are trying to explain the universe

in fact physicists not caring about mathematical rigor is a good thing because it is basically due to that fact that new mathematicial discoveries and progress are made

[vital bane]

Such as the Lebesuge Integral, Fourier series, Spectral theory, Mirror symmetry and a lot more stuff

experimental physics goated

without data, there would be no problems

[naive lava]

well you can't really solve the pendulum without this approximation

[vital bane]

at least not in closed form

[naive lava]

buuut there are physicists who use symplectic manfolds to find general patterns in motion

[vital bane]

https://en.wikipedia.org/wiki/Spectral_theory

actually it seems Spectral Theory came first

that's crazy

same thing happened with differential geometry and GR

[naive lava]

hilbert was a goat

[vital bane]

it's actually beyond insane how interconnected mathematics and physics are and how ideas flow in both directions

[naive lava]

In a seminar by von neumann, he explained hilbert space is the basis for qm, and then hilbert asked, what's a hilbert space

[vital bane]

my point is, people use ideas from physics to solve problems in mathematics

the connection in the other direction is what I was emphasizing

[naive lava]

one thing that amazed me the most was use of homotopy in physics

like how in the world

[vital bane]

where??

[naive lava]

SO(3)'s fundamental group is Z_2, and that's why spin-1/2 exists

[vital bane]

electron moment

[naive lava]

in 2D, SO(2)'s fundamental group is Z, and that's why anyone's exist

I'm definietly sure that i spelled that wrong

[vital bane]

anyons?

[naive lava]

idk what they are called

spin 1/3 spin1/4 things

the solid state guys love em

[vital bane]

huh interesting

[tender cobalt]

and assume c = 1

[vital bane]

hbar = c = 1 excuse me

[tender cobalt]

why do they do that man

why do they hate symbols

😔

why not create some algebraic object instead which have c and hbar encoded on them or something

[vital bane]

that doesn't make sense

[vital bane]

it's called natural units, they just change the units from SI to natural units to make calculations easier, and equations prettier

[tender cobalt]

forgot that in physics, theres nothing "exact"

[vital bane]

https://en.wikipedia.org/wiki/Natural_units

[vital bane]

I don't understand what you mean this has nothing to do with approximations

[tender cobalt]

While natural unit systems simplify the form of each equation, it is still necessary to keep track of the non-collapsed dimensions of each quantity or expression in order to reinsert physical constants (such dimensions uniquely determine the full formula).

is it only me that i suck at keeping track

or physicists are good at keeping the track

of which dimensions

[vital bane]

when you have 60 page calculations, it's better to focus on the tensors and stuff instead of the physical constants

[tender cobalt]

why do they get so lengthy 😭

[naive lava]

the beauty is that you don't keep track

you write out multi line integrals

if you try to add those symbols in too, you'd probably lose track of them somewhere

cos units make less and less sense as you push trough your calculation

but if something like phi^4 is off, you'd notice and go back easily

then at the end, you can just add units back

[tender cobalt]

makes sense

[vast jackal]

that's because teachers don't explicitly explain how important or idk

[keen orbit]

Is lang's book on abstract algebra good ?

I heard people don't like dummit and Foote because it is lengthy/wordy

So what are some better options

[vital bane]

some people say it's subpar and there are better options, and others say it's amazing

[remote sparrow]

lang is good for a certain audience

[vital bane]

I love Dummit and Foote because it has awesome exposition and amazing exercises

[remote sparrow]

if you're talking about the GTM book

[vital bane]

[vital bane]

oh yea lang has two algebra books

you should specify

[keen orbit]

What does GTM stand for

[vital bane]

[remote sparrow]

graduate texts in mathematics

[keen orbit]

Ah no the one I am talking about is UGTM

[remote sparrow]

*utm

[keen orbit]

oh alright then utm

[vital bane]

UM*

(jk)

[keen orbit]

I just made up this abbreviation

So what about the utm book

[keen orbit]

Is this what you were talking about

Or you were talking about the gtm one

[vital bane]

no I was talking about Lang's graduate algebra book

it's just called "Algebra"

by Serge Lang

[remote sparrow]

#book-recommendations message

i like these algebra books

[vital bane]

Dummit and Foote hater

[remote sparrow]

i think dummit and foote is fine; it's just not my first choice for an introduction

[keen orbit]

Alright I will check these

[vital bane]

what do you think of Gallian then?

[keen orbit]

One more question, what about rotman's utm book

[remote sparrow]

rotman hasn't published a utm

[mellow wren]

Horrible book

[keen orbit]

I came across a book called "a first course in abstract algebra "

The name of the author is Joseph J. Rotman

[remote sparrow]

it's an abstract algebra book that tries to be like a calculus book is my impression

[remote sparrow]

utm and gtm are book series under springer

they're not generic abbreviations

[keen orbit]

Ah I see

So I am abusing notation rn (just like treating dy/dx as a fraction )

The what about the undergraduate textbook of rotman

[mellow wren]

First abstract algebra book I tried to read and I feel like it taught me nothing lmao

[remote sparrow]

https://old.maa.org/press/maa-reviews/a-first-course-in-abstract-algebra-with-applications

seems interesting

[naive lava]

No. dy/dx is a fraction

[vital bane]

Non-standard anal moment

[naive lava]

Or covector field moment

[rich sun]

How is that a covector field moment

[wispy bison]

Does anyone happen to have any book recommendations for zero-knowledge proofs?

[grave flume]

I am reading about Mobius function and came across Euler totient function, Kronecker delta (δ), the Liouville function (λ), and the number of distinct (ω(n)) and total (Ω(n)) prime factors of n.
Can someone please suggest me a book where I can start with these from basics? Having some problems to solve would be a huge + as well.

[vital bane]

@remote sparrow Have you ever gone through this?

this seems like a nice book

also I found this

[molten gulch]

LMFAOOOOOO

[vital bane]

@heady ember I found your account on reddit, it seems you are a closeted engineer

[marsh ingot]

Like Rudin

Im joking around but Im gonna read Grandpa Rudin soon

[vital bane]

I myself have accquired a copy of baby Rudin

[marsh ingot]

I should do the same

Or at least Papa Rudin

[naive lava]

My prof said it's kind of an okay book but others are better

[gray gazelle]

pinter

[uncut salmon]

I need suggestions for a book of analysis 2 that covers: metric spaces, continuity and differentiability of functions in R^n, ordinary differential equations (of degree 1 is enough), integration in R^n without being too rigourous from a measure theoretic point of view.

[timber holly]

Justin thalers I assume your getting into cryptography

[stray veldt]

how about https://toc.cryptobook.us

[remote sparrow]

schroder is the only book i can recall that does everything you mention, although integration in R^n is developed after measure theory

https://www.amazon.com/Mathematical-Analysis-Introduction-Bernd-Schröder/dp/0470107960

[heady ember]

[heady ember]

If you're gonna read Schroder, I recommend you compliment it with another book like Rudin for challenging exercises, which Schroder only has a couple each chapter.

[old elk]

HAHAHAHAHAHAH

[naive lava]

I'll take alg top next year, am I cooked

[keen orbit]

hmmm i see

[keen orbit]

then do you have any recommendations other than rotman D&F and artin ?

rn i am trying to look into many books to choose one of them after that and work with it

[floral lantern]

If you want a more abstract perspective aluffi’s undergrad book (or maybe even the grad book depending on your preparation) is excellent

[keen orbit]

isnt exposure to a first course in abstract algebra a part of the preparation for the grad book ?

or is that not strictly necessary

so does the grad book cover everything from the ground up but with a faster pace than undergrad and continues to cover deeper content?

or does it start from some point that assumes knowledge of the content of a first course in abstract algebra

[floral lantern]

the grad book is entirely self contained

admittedly most students working through it would have seen abstract algebra before but if you're a strong student this is not necessarily necessary

but I would probably recommend the UG book

[keen orbit]

alright tysm

[naive lava]

no no that was about something else

but I'm using aluffi rn and it's fucking amazing

[keen orbit]

ohhh ok

[keen orbit]

which one ?

[naive lava]

I am in love with cat theo sooo yk

[keen orbit]

the ug one ?

[floral lantern]

This is a hate crime

[naive lava]

ch 0

[keen orbit]

ohhh

[floral lantern]

(Category theory traumatizes me)

[keen orbit]

have you done abstract algebra before this

or this is the first time ?

[naive lava]

I don't really really know it

but from what i've seen I's pretty cool

I like things that generalize and connect things so I'm kinda in lucj

[naive lava]

eeeeh

not rigorouslty

I'm doing physics so yk

[torn blade]

oh yh i wanted to ask why some people in the server have beef with Hatcher’s alg top

i thought it was quite good (in fact the only alg top book i can actually enjoy…) but i wanted to know what’s wrong with it and if there’s any better alternatives.

[naive lava]

My prof's main concern is that there is no cat theo

and if you wanna use alg top and not just study it, you should be able to connect it to other things

[torn blade]

oh yeah i need to revisit alg top at some point because i didnt do that many exercises so it didnt fully sink in for me

so i might switch to a diff book but not sure which

[gray gazelle]

I recommend Topology and Groupoids for AT

[keen orbit]

Ohh I see. Then I will give it a try too

Tysm everyone for your great recommendations

[naive lava]

rotman might be a good follow up

orrr if you're daring, go for may

but fair warning, may is very abstract

[torn blade]

im not daring lol

what about Munkres?

[naive lava]

I can only speak for Peter May’s style because I know the man and attended many a lecture from him when I was at Chicago—once an audience member asked if he could draw a picture of what he was describing and he drew a commutative diagram. Homotopy theory as a whole is sometimes pretty visual and often abstract, Peter May is almost never visual and typically hyper-abstract

quote from reddit

[naive lava]

I didn't hear much about it

I'd go for rotman if I were you

My plan is rotman -> may 1 -> may 2

[trail hemlock]

bro rotman is so peak

[indigo mesa]

Rotman is good but the exercises are too easy and not very instructive imo

Supplement it with Hatcher, for examples as well

Hatcher is actually pretty good when you don’t have to read it back to front

[remote sparrow]

have you looked at bredon?

[remote sparrow]

bredon and tom dieck are in the pins as well

[naive lava]

I haven't heard brendon before, how is that

[remote sparrow]

can't really say much about it

i only know about it from pins

#book-recommendations message

[willow merlin]

book that

explains

affine spaces

[dire stone]

what is a good second algebra book? i have pinter now but want more

[remote sparrow]

dummit and foote

[dire stone]

i’ll check it out

[near wagon]

What are some good linear algebra books for someone looking to apply those skills in optimization? I’ve taken a linear algebra course before. Just not sure if I should dive into numerical linear algebra. Or something else like Linear Algebra done right (might be too theoretical?).

[vital bane]

FIS has a perfect balance of applied and pure Linear Algebra

Linear Algebra Done Right is better suited for someone trying to do Functional Analysis after LA

[naive lava]

nah that's lax's linear algebra

[torn blade]

starts off with diff top, interesting

looks challenging but ill go for it. should i supplement the diff top parts with anything or is it ok to just read it on its own

[remote sparrow]

i would assume it's self-contained

rotman's probably still good to read, but as timo said, you'll need more challenging exercises

[vital bane]

it's Axler, Lax and Halmos

[wispy bison]

Thanks! I’m just looking to learn more about it after watching a Youtube video about it

[wispy bison]

Thanks! I’ll check this out as well

[scarlet walrus]

Any free books online about visualising math?

[timber holly]

I started with Dan and then David

[remote sparrow]

as in saracino and then dummit?

[timber holly]

yes

[tender cobalt]

any algebra book that are both undergrad + graduate level? something like steve roman advanced linear algebra?

[vital bane]

Not sure, I think the main qualms people have with it is the amount of category theory, or lack thereof, as dogu said

[vital bane]

[tender cobalt]

any other than this its too fat 😭

[vital bane]

But focus on Munkres until you finish it

[vital bane]

fat = more content = more knowledge

[tender cobalt]

what about aluffi algebra notes from underground

it covers till some galois theory

[vital bane]

I have heard good things about it but I have not checked it out myself

[tender cobalt]

can i learn commutative algebra after that book

[tender cobalt]

oh

[vital bane]

you got this mate

[vital bane]

D&F has commutative algebra and basic algebraic geometry

[tender cobalt]

im doing a crazy study routine, linear algebra, algebra, topology, and analysis

[vital bane]

even some homological algebra

[tender cobalt]

whoa

[tender cobalt]

Hot stuff

[floral lantern]

Category theory 😦

[vital bane]

Part 3 is module theory and vector spaces, part 4 is field theory and galois theory

[tender cobalt]

but how is it written? is the book's writing nice and pedagogical?

[vital bane]

left as an exercise for the reader

[floral lantern]

D&F is written well, just dry

[vital bane]

imo it's amazing

[tender cobalt]

What about aluffi chapter 0? he takes categorical aproach

[vital bane]

I love the writing

and the exercises are awesome

[floral lantern]

Let me out

[vital bane]

and there are lots of exercises

[floral lantern]

I hate category theory

[tender cobalt]

hmm

[tender cobalt]

Cold

[vital bane]

so you'll get lots of practice

or you could just use Lang's "Algebra" right off the bat @naive lava did

[tender cobalt]

but he yaps a lot

[vital bane]

does he?

[tender cobalt]

he be like "you shouldnt read this book until you read my undergrad book"

[floral lantern]

Lang 😨

If you want just group theory, herstein’s treatment is exceptions

[tender cobalt]

i want emphasis on ring theory

[vital bane]

Herstein is weird imo

[floral lantern]

But as I understand the rest of herstein is very eh

[vital bane]

I mean it's well written

but weird

which is probably due to how old it is

[floral lantern]

Are you aiming for algebraic geometry?

[vital bane]

Lang the Rudin of Algebraor at least that's the vibe I get from what people have said about it

[tender cobalt]

yes

and algebraic number theory

[floral lantern]

Aluffi is written with an eye towards geometry

[tender cobalt]

which one

[floral lantern]

(Aluffi is a geometer)

Both books but moreso the graduate book

[vital bane]

What about

[floral lantern]

Depending on your preparation it’s not impossible to just jump to the grad book

[floral lantern]

This is an actual commutative alg book tho

First you have to learn alg

[vital bane]

Right yeah

[floral lantern]

Most people use what

[vital bane]

imo there's no point in rushing to alg geo

[vital bane]

Macdonald?

[floral lantern]

Atiyah-Macdonald?

Yes ah

[vital bane]

I've also heard Matsumura

being used

[tender cobalt]

Okay I think I'll go with aluffi notes from underground

[plush rain]

mura

[vital bane]

Muda

[tender cobalt]

since rings, modulars, groups, fields & galois theory is covered

[floral lantern]

This is a rings first book so you may find it more to your liking

[vital bane]

interesting

[tender cobalt]

There is also hungerford's intro algebra book which is rings first

[floral lantern]

Yeah but hungerford is bad

[tender cobalt]

But I couldn't find a clear pdf lol, all pdfs are like blurry af

[floral lantern]

💀

[tender cobalt]

There will be overlaps with my roman study as well I guess

on module theory stuff

Alright thanks guys ill go for aluffi notes from underground

[strange tree]

Rotman Advanced Modern Algebra

[naive lava]

Nah i gave up on that shi

That took 5 years of my life

[tender cobalt]

is that a good book to start algebra 🤔

[strange tree]

didnt you asked for smth UG + G lvl?

Id say you can read it as an ug tho

[tender cobalt]

yea

[naive lava]

Just use aluiffi

Goated book

[floral lantern]

Tbh I think you can just read Aluffi grad alg

If you’ve already seen some linear algebra

And other proof based stuff

[tender cobalt]

but isnt aluffi is known for bad exercises 😔

[floral lantern]

???

Aluffi is known for great exercises what

[tender cobalt]

from the pinned messages

[remote sparrow]

#book-recommendations message

#book-recommendations message

[tender cobalt]

and ive seen some reviews elsewhere as well

[remote sparrow]

which one

[floral lantern]

The grad books

[vital bane]

Aluffi notes from graduate underground

[tender cobalt]

graduate underground 🤣

[tender cobalt]

Ay rotman is looking cool ngl

[naive lava]

They are good imo

[vital bane]

From Rotman's Algebraic Topology book:

[remote sparrow]

#groups-rings-fields message

#serious-discussion message

[tender cobalt]

"earlier" ? 🤣

[vital bane]

bro is savage

[floral lantern]

Perhaps I am a liar

The ones I’ve seen are ok though (stuff like weak dirichlet)

Thank you for the links

[remote sparrow]

the first edition is self-contained, but the problems are maybe on the easy side according to some

the second edition is the copy i have

it's not as self-contained as it refers the reader to his ug book for more elementary material

[modest kite]

Hello, what should I study for math olympiad? I have one whole year

And i want to work everyday without pause

.

[wet sentinel]

what about the first book/part of the third edition

is it self contained like the first edition ?

[tender cobalt]

What would be the axler/friedberg analog of algebra

[grim ore]

there is a lot more common/standard/famous texts for algebra but most would say something like D&F (more like friedberg) and or Artin (more like Axler), or I would say baby hungerford and get kicked out of the counsel of math for doing rings and fields before groups, and others would say Aluffi and wish to intimidate people, someone insane would say Lang and will likely go on to do great things, by the end of the day just do what you suits you best

I also know that you are a huge shifrin fan, which also probs mean youd love his algebra text too

He does algebra from a more geometric perspective and honestly I loved reading algebra from a different perspective after finishing hungerford

[grim ore]

it does also coincide with the fact that I kinda like geometry to some scale tbf

[remote sparrow]

it still assumes you know some algebra going in

however, it is a little more self contained with respect to the requisite number theory

[wet sentinel]

how much knowledge

[remote sparrow]

you should be familiar with groups and rings

https://a.co/d/5NmneV8

btw the 2nd edition of rotman is finally at a reasonable price

hurts a little that i paid a little more than what it's going for now but i'm here to spread the word

[wet sentinel]

so for example is it sufficient if i am familiar with the content of chapter 1 of D&F and a bit of chapter 2 ?

for the group theory part

[wet sentinel]

it definitely hurts, but i wonder how much was its price when you bought it because now after the price went down it is sold for 90$

[remote sparrow]

chapter 1? no. you mean part 1?

[wet sentinel]

no , so my point is if rotman's book can be used to learn abstract algebra without exposure to a first course before that

[remote sparrow]

not the second or third editions

[remote sparrow]

like $105-110

don't remember exactly

after shipping and tax

i used a $10 coupon too

wasn't amazon

[wet sentinel]

ohhh , i think it is still a bit expensive at 90$ but my opinion isnt accurate since i have never bought a math book before xD

[remote sparrow]

2nd ed is 1000+ pages

and a nicely made sewn bound book

opens super easily and lays flat

[wet sentinel]

in this case i change my mind

[wet sentinel]

usually one fights with the book before it lays flat

sometimes it doesnt even after that

[wet sentinel]

alright tysm

[remote sparrow]

#advanced-lounge message

@wet sentinel

[wet sentinel]

wow the physical copies of books are great

[remote sparrow]

in at least some books, yes

[wet sentinel]

much better than studying from pdfs

[remote sparrow]

@mossy flume not sure if you personally own a copy of advanced modern algebra but this is the lowest i've seen this edition go for in a while

[remote sparrow]

@crimson leaf

[naive lava]

just because of this, im considering dumping my whole savings on books

[remote sparrow]

i am still looking at e-ink tablets, but the technology isn't quite there yet

[molten gulch]

yooooo\

part of me wants to splurge on that

👀

[remote sparrow]

on books or e-ink tablets

[molten gulch]

on book

[naive lava]

those are okay i guess but i usually flpi trough the book quite a lot and they're missing that

[remote sparrow]

i think they'd be a good way to save money on buying novels

[wet sentinel]

idk maybe i should spend some money on books in the future after seeing this

[remote sparrow]

not that i've bought novels except when they were dirt cheap

actually i have very little fiction on my shelf

but i read most fiction online or on my pc

[remote sparrow]

it's like an addiction man

[naive lava]

I don't have time to piss, let alone read novels

[wet sentinel]

bro is breathing math and physics?

[remote sparrow]

physics grad student

[naive lava]

hey hey hey imma stop you right there

I hate all kinds and forms of math

[wet sentinel]

yea but he is studying algebra by aluffi too

caught you red handed

[naive lava]

mathphy moment

[mossy flume]

OOOOO I'll consider it

[wet sentinel]

😯

thats a bold claim 🔥

[gray gazelle]

[stable axle]

Does anyone have recommendations for algebra books which take a historical approach to building the theory? I've been convinced that getting some good historical perspective on the development of the field will help me understand better the formulations of the definitions and theorems (especially when it comes to Galois theory)

I'm not going to be taking any classes in algebra until at least next year so this is really just for the sake of my own understanding of the subject. When I originally learned it there was no motivation provided for anything. Just a terse definition -> theorem -> proof structure we're all too familiar with. But I've recently realized I feel like I know basically nothing about groups or rings or fields outside of the base definitions and properties about them

[floral lantern]

Historical perspective!= historical approach

Historical approach is messy and I abstract and weird

The modern notion of a group shows up much later than the development of Galois theory

And galois’s Galois theory barely resembles the modern theory

[vital bane]

what a group was back then:

Literally just S_n

Cayley's Theorem moment

[floral lantern]

Lmao sotrue

[dim sierra]

Edwards Galois Theory

[pliant wadi]

If I wanna look at the more computational/physics-y aspect of Ergodic theory, where should I look?

Like, ik its origins lie in statistical mechanics

But like, modern Ergodic theory, what sort of computational problems are interesting to people working in it?

[stark lion]

Is it bad that I am starting to prefer the PDF more than the physical copy

[vital bane]

Yes

PDF is good, but physical copies are better

[tired frigate]

Any book recomendation for me to start mechanical Engineering

[vital bane]

Maybe you will get better recommendations in the engineering servers in #old-network

[gray gazelle]

Physical copies got that crisp PDFs don't have

[foggy spindle]

Any book recommendations for starting to learn calculus?

[rich sun]

stewart's calculus

[foggy spindle]

Thanks

[tender cobalt]

oh yeah he also takes ring first approach i almost forgot! yeah ima check his book out

[gray gazelle]

When I first was getting interested in mathematics someone recommended Spivak. I think his book is good, but it was a useless rec for me since I had never seen proofs before.

I'm not actually sure when you would want to start there, or use it as a teaching text. If you have a group of students who know how to write proofs as incoming freshmen there is a good chance they've taken a calculus course before. I think Shifrin, speaking of him, taught with Spivak's book at UGA, but I don't have any idea how the class was structured or who the audience was.

[remote sparrow]

spivak is often used for honors calculus classes designed for first-year college students that have previously seen calculus in high school. there are also honors classes that don't assume any calculus background which teach with a mix of spivak and books like stewart for routine problems.

[stable axle]

I never even knew about this to begin with and would've been happy to have my instructor mention it lol

Thanks for the explanation

I'd still like to give it a look even if it might not be the optimal way to learn the theory

I have already learned it once after all so at this point I'd just like to get some perspective on everything

[stable axle]

Thanks

[gray gazelle]

Interesting! Thanks for that, I had no clue it was used for that - certainly makes sense as a use case

[tender cobalt]

Question, guys, can i jump and start from Rings chapter in artin

and complement it with aluffi notes from underground

[slender cargo]

..why would you want to do this?

Might as well choose a book that goes rings first

[tender cobalt]

is there no rings first book other than aluffi and hungerford and shifrin?

[slender cargo]

I imagine there are others. But why the interest in doing rings first?

I know some instructors think it's more pedagogical. Gives more examples of stuff you're familiar with. But most books have groups first, since a ring is defined with respect to a group

[tender cobalt]

hmmm

[floral lantern]

If you’ve seen number theory before rings first isn’t really necessary imo

[wet sentinel]

advanced modern algebra by rotman starts with rings

idk if it is good or no

[tender cobalt]

doesnt he start with grups

[wet sentinel]

the third edition starts with rings

the third edition is divided into 2 books

it starts with rings

i am now checking the table of contents of the second edition

[wet sentinel]

this one starts with groups

[wet sentinel]

so maybe you are talking about this

keep in mind that i dont know about it so idk if it is good or no

[wet sentinel]

but i only know that this edition starts with rings

[dawn shoal]

I'm looking for an ODE textbook covering the following topics (best if all, but that's not a must):

• Initial value problem. Equations of higher orders. Methods for scalar equations: separable variables, linear equations, Beroulli equation, complete differentials.
• Local existence and uniqueness. Picard–Lindelöf theorem. Dependence on parameters and initial values. Extending a solution.
• First order linear systems. The space of solutions. Wronski determinant, Liouville theorem. Linear equations of higher orders.
• Autonomous equations and flows. Vector fields. Lyapunov stability and asymptotic stability. Phase space and phase curves. Phase curves for a 2-dimensional linear system. Pendulum. Lyapunov stability of solutions. The Lotka-Volterra system of equations.
  I've covered: real multivariate analysis, basic measure theory, differential manifolds, all linear algebra that will be necessary for studying ODEs at this level. At the moment, I'm following Gabriel Nagy's "Ordinary Differential Equations", but it seems to lack some of the things I've listed, e.g. no work by Liouville or Lypaunov seems to be covered.

[tender cobalt]

alright thanks

[tender cobalt]

Do you mean hungerford intro abstract algebra or the GTM text?

[slow roost]

They referred to "baby Hungerford" which is the undergrad text

[tender cobalt]

Oh

I haven't been able to find a clear pdf of that text

All are blurry AF

Oh wait hungerford algebra the GTM text is apparently self contained

Ay it's looking like Steve Roman of algebra

[meager laurel]

Any ebook recommendations for high-school level math?

Just wanna learn something alongside my general studying

[near jewel]

"How to solve it" and "How to prove it" would probably be the recommendations.

[meager laurel]

Thanks

[near jewel]

It's more the thinking than the further knowledge.

If that's what you're thinking about.

[meager laurel]

It helps with analytical skills?

Ohhh

Yeah this will help me

Thanks man

I study engineering

[near jewel]

Will work, those two are pretty general.

[meager laurel]

I checked google and found pdfs, thanks bro

How to solve it seems good for not just math and how to prove it is good cuz ill have discrete math at university

I appreciate it

Thank you very much

I will start with "how to solve it" first

[fresh skiff]

Same

[tepid wind]

Can anyone recommend books for highschool math competitions?
Problems textbook preferably
Combinatorics, number theory, geometry, algebra

[naive lava]

titu andressicu has amazing books on problem solving

[cloud imp]

I also found AoPS website of previous AMC contest questions to be extremely helpful

[tepid wind]

Thanks! I'll make sure to check them

[remote sparrow]

@naive lava is it true that sakurai falls off in the chapters he didn't personally write? also, thoughts on cohen-tannoudji?

[naive lava]

absoulutely true take

it's still good

but the first 4 chapters are so goated

before that I've readen like 1,5 QM books

couldn't understand how everything works, the big picture

then i picked up sakurai

it was so good i couldn't put it down

even made a full solution manual myself

I haven't read cohen tannoudji but i heard it was good

I doubt it'll beat sakurai tho

[remote knoll]

I looked on MO and saw that Coddington's "Theory of Ordinary Differential Equations" was recommended. I downloaded a copy, and it does seem to cover most everything you requested. Hope this helps.

[dire smelt]

im take that advice for myself lol

[dawn shoal]

Thank you! I’ll take a look at it tomorrow 🙏

Much appreciated

[final swallow]

Art of Problem Solving Books

[remote sparrow]

@naive lava i found a pdf of smythe that has a solutions manual included

[naive lava]

☠️

[remote sparrow]

https://old.maa.org/press/maa-reviews/introduction-to-real-analysis-2

https://heil.math.gatech.edu/6337/spring11/

https://heil.math.gatech.edu/real/

[urban relic]

Hi, i'm looking for some book / article recommandation to learn about Borel-Weil theorem.

[sly spade]

Anyone know where i can find ∫ln(x!)^n

?

[sly spade]

Ye theres no result

[signal mountain]

why do you want this

and is it meant to have limits

[sly spade]

Cuz ∫x! dx

[signal mountain]

that does not clear it up...

[molten gulch]

Integrate the gamma function

Possibly

[sly spade]

We dont rlly what the gamma function even is

I mean integrating t^x*e^(-t)dt isnt possible

[rich sun]

why not

[sly spade]

Try integration gamma(x) u get x*gamma(x+1)

Not integrating the gamma function

The things inside

[rich sun]

it is possible because the integrand is continuous

[willow saffron]

can somebody recommend a well structured data science book?

[graceful dawn]

I am a software professional occassionally reads math books. I want to know whether 'Burton Elementary Number Theory' is a good read for me?

[subtle violet]

what books have you read prior to this?

[graceful dawn]

Sorry wrong chat for the deleted message
I am an undergraduate in Engineering field. Knows basic math and might be able to understand these advanced concepts.

[subtle violet]

hmmm

[graceful dawn]

I just skimmed first two chapters, didn't find it difficult in understanding the examples. But before going too deep I wanted to make sure my time is well spend.

[subtle violet]

i haven't read the book myself, i'm just skimming it rn, but yeah if you find the introduction difficult it may be best to pick up a gentler book that teaches basics of proofs. but it sounds like you don't have that problem

they jump into some proofs pretty quickly

[graceful dawn]

The first chapter is something I studied in my school days but here a little more deeper. From prime numbers it's going deep.

I find it's more interesting than Tao's books.

[subtle violet]

which of tao's books did you take a look at?

(just curious)

[graceful dawn]

Analysis 1

I am talking about general , not number theory.

[subtle violet]

yeah real analysis can be pretty dry, it's very important and useful for understanding other subjects that build on it though

elementary number theory on the other hand i think is interesting in its own right, and very accessible

and probably more useful for software professionals (i am one too)

[graceful dawn]

I want to supplement it with more exercises, any links?

[subtle violet]

supplement what, the burton book? or analysis

[graceful dawn]

Burton

[subtle violet]

would probably have to ask someone else, i haven't read any books on elementary number theory, although i guess i've used Applied Combinatorics by Keller and Trotter as a reference, which i do recommend if you're interested in something adjacent

[graceful dawn]

Combinatorics was a difficult subject for me and probabilities too.
Let me check Keller.

[subtle violet]

the whole book is available for free on the internet

https://www.appliedcombinatorics.org/book/app-comb.html

[graceful dawn]

Probabilities I studied from Sheldon Ross, is it better in Keller?

[subtle violet]

the probability section in keller is very short and i doubt it is harder than anything in ross, everything is on finite probability spaces

[gritty steppe]

ok

[tender cobalt]

Is Isaacs algebra good

[remote sparrow]

@loud cradle

[plush rain]

tragic

[pearl sparrow]

What would be an intuitive textbook to learn statistics from that you would recommend?

[willow merlin]

which book covers matrix representation of a linear transformation wrt certain bases?

[molten gulch]

any text on linear algebra should

FIS, Lay, etc...

[willow merlin]

if possible one book that covers this theorem

[mortal ore]

why

i mean seems like you already are aware of it

[willow merlin]

is for a friend

[whole latch]

Books are not for maths

[willow merlin]

that has to cover matrix rep of a linear transformation wrt to certain bases

he is engineering

[mortal ore]

what?

books are for anything

[molten gulch]

yes they are

[whole latch]

True but

just telling you

[willow merlin]

wdym?

[mortal ore]

nvm if its for a friend

[mortal ore]

yeah but ur not right

[willow geyser]

If i am to start reading what would be a book to start with

[mortal ore]

whats ur background with math

[willow geyser]

Hs math

I wanna learn more before uni

[mortal ore]

does this include calculus

[willow geyser]

Yes i learned clac

[mortal ore]

if you wanna start learning how to prove stuff, ive heard richard hammack's Book of Proof is good

[whole latch]

Books cover many things

[willow geyser]

Okay ill check it out ty

[whole latch]

but when it comes to math, clarity is key.

[mortal ore]

i have no idea what ur saying

[whole latch]

those need precision, not just words.

[willow geyser]

Clarity is important in math books

[mortal ore]

well yeah

[willow geyser]

Im joking

[mortal ore]

has nothing to do with what theyre saying

idk what clarity has to do with books

[willow geyser]

Same tbh

[whole latch]

it’s a requirement.

[trail hemlock]

but what if u fill the book with math

[whole latch]

isn't optional, especially when dealing with proofs or concepts like matrices. Without it, chaos ensues.

they fail to convey the truth.

they must be more

[trail hemlock]

thats why sometimes u draw a picture

or include a diagram

but i disagree that books aren't sufficient to convey mathematical ideas, unless im not getting at what ur saying

[whole latch]

"Precisely. A diagram can bring clarity where words fail. But remember, the diagram itself must be accurate, just as much as the equations.

'

my quote

Books can cover many things, such as quotes

[remote sparrow]

that guy in the lower right is nathaniel johnston right

he wrote books based off those lectures

[trail hemlock]

do u know everthing related to books 🥀 😭

[whole latch]

Not everything, BlackBeard. But I know that the purpose of a book is to convey knowledge clearly and precisely. If it fails in that, it’s nothing more than a collection of pages.

Anyways, I am going to end here.

See you guys later.

[remote sparrow]

https://tenor.com/view/mega-brain-big-brain-math-pineapple-gif-gif-25841999

[remote sparrow]

no

[full cairn]

AI or trolling? probably both

[remote sparrow]

pre-uni role

[full cairn]

Look at his history

[trail hemlock]

hopefully trolling

[final swallow]

I prefer how to prove it by daniel velleman

[naive lava]

hey i think i should mention this in regards to sakurai

please please please learn how symmetries work and determine the theory

it's the sole useful thing we use in QFT

whole thing is built on the idea of symmetry

[naive lava]

especially the gauge part

I did not care in my first pass

it was just a funny math thing

didn't know it was the entire idea behind SM

[remote sparrow]

gotcha

[vital bane]

Time to pick up an entire book on representations of Lie groups

[naive lava]

make sure it has graded lie groups too

[vital bane]

Interesting, that comes up a lot in QFT?

[naive lava]

if you want susy or sugra or string yeah

entire idea is that no-go theorems

coleman mandela comes to mind

[remote sparrow]

https://tenor.com/view/sussy-baka-gif-23628158

[naive lava]

they say that you cannot expand lorentz group without causing catasthrophe

but some folk decided to say

hmmmmmm

what if

spinors

[vital bane]

I see okay

[remote sparrow]

right now i'm only interested in basic qm just cuz, even though nielsen and chuang is mostly self-contained

[naive lava]

well if you truly understand QM

then QFT is just a "slight" upgrade

namely infinitely many more dimensions

[vital bane]

instead of 2n-dimensional symplectic manifolds,we now have infinite dimensional one representing the config space?

[naive lava]

you just stick a QHO in each point is space(-time)

[vital bane]

right and that gives us infinite degrees of freedom

[naive lava]

yeah that's the main idea

[dusk nova]

Dragonlance chronicles was a good fantasy series

Similarly, the Death Gate Cycle was a good read

[remote sparrow]

i felt the last book in this series was mid when i read it in HS

[dusk nova]

I thought so too, I preferred some of the earlier books.

[remote sparrow]

have you read the kingkiller chronicles

[remote sparrow]

https://youtu.be/VUh3Pu5RR4U

[leaden panther]

Hey guys can someone recommend me any books that I can get on my birthday

[remote sparrow]

what math are you already familiar with

is there an upper limit to how much can be spent?

[leaden panther]

Like 3k is the upper limit

[remote sparrow]

what currency

[leaden panther]

Rupees

[leaden panther]

I want like first year ungrad calc

[remote sparrow]

i think thomas' calculus seems to be rather popular in india for some reason (it's perfectly fine from what i've read from it, i just find it strange that that's specifically considered the standard text)

i'm sure there are plenty of used editions floating around

@vital bane

https://www.youtube.com/watch?v=9Ki_Pcc5LMM

unrelated, this is a nice video

i was watching it a little bit ago

[leaden panther]

@remote sparrow is spivak good for me??

@remote sparrow can u send me the link to purchase for thomas calculus

[remote sparrow]

are you willing to learn how to read and write proofs if you aren't already familiar with them? also, i think its list price exceeds your budget by a huge margin

[leaden panther]

Ok

[remote sparrow]

you can probably find it on amazon india (i'm from the u.s.)

[leaden panther]

Ok what's the book cover??

[remote sparrow]

the edition doesn't really matter

[leaden panther]

Can u send me the cover image of any edition

[molten gulch]

https://www.amazon.com/Thomas-Calculus-14th-Joel-Hass/dp/0134438981

[remote sparrow]

they change the cover picture with each edition, but one commonality is that they have "Thomas' Calculus" on the cover always

[molten gulch]

Our uni used thomas and last year switched to stewart

we liked thomas more and have a physical copy of it bc it was cheaper to get at the time

[remote sparrow]

did they say why?

[molten gulch]

idk why I cannot stand stewart

[molten gulch]

idk I haven't asked around

[remote sparrow]

i learned from stewart, but i think thomas is going to be my default recommendation going forward

[molten gulch]

yeah

[remote sparrow]

i heard the publisher behind stewart's calculus makes deals with universities to have their book adopted

not sure how true that is

[trail hemlock]

anything for the damn integral house

[remote sparrow]

[molten gulch]

Thomas

stewart

as a definition/theorem example

[remote sparrow]

stewart is the only guy who became a multimillionaire off of textbook sales; not sure what his secret was

[molten gulch]

but I mean even the writing is quite similar, problems are similar,etc...

[trail hemlock]

larson my goat bro

[molten gulch]

I just...prefer thomas, maybe bc it was my first "proper" maths textbook

idk

[trail hemlock]

i heard stewart assassinated ppl who didnt use his book but idk how true that is

he never left witnesses, after all

[remote sparrow]

well, in thomas this definition is upfront, while stewart puts this at the end of the section

[molten gulch]

yeah

well no

both were 4 pages into the chapter

oh wait you said section

I'm SO tired right now, sorry

[remote sparrow]

i think there are more problems to prove in thomas as well

i think the problems plus sections and little project snippets in stewart seem cool tho

[molten gulch]

yeah

in other news: how fucking washed am I that this actually felt "new" until I realized this was basically trivial

[remote sparrow]

i like thomas' explanation for green's theorem

and other multivariable topics

[molten gulch]

I didn't read either for multivar and purely went off my prof's notes

I kinda feel like I should read them...or maybe solidify my analysis and go read a multivar analysis chapter

idk what'd be better

[remote sparrow]

i saw some people say stewart was dogshit for multi (i actually was assigned larson for multi at community college), and going through stewart and comparing to thomas and larson, i have to agree

[molten gulch]

How so? /genq

what makes it worse in your opinion

also I skimmed larson and kinda liked what I saw, how would you compare it to stewart and thomas?

[remote sparrow]

i think the calc 3 formulas and theorems weren't motivated very well

[remote sparrow]

it's not bad, though i'm a little sad i have the 11th edition of larson (which moved the proofs in the appendices online). i got the multivariable calculus version of larson when i didn't know any better about book buying.

i like the suggestive pictures for multiple integration

there's a little arrow to suggest "sweeping out" volumes when doing volume integrals

[leaden panther]

Btw is spivak book pdf available online??

[remote sparrow]

i think thomas proves more things and the proofs are generally more readable imo

[remote sparrow]

yes

yes to your edit as well

[leaden panther]

Can someone pls verify the pdf I have of it

[tender cobalt]

ngl thomas and stewart are kinda different

thomas more theory focus than stewart

[tender cobalt]

okay guys after searching so much for algebra, ive come down to Isaacs Algebra A Graduate Course or Hungerford Algebra, both texts which says theyre self contained in preface. Now which one should I go for 😭

[naive lava]

hear me out

have you considered jacobson?

[remote sparrow]

he's never had a course in algebra before

he can try jacobson if he wants

as far as i can tell, he's looking for something "challenging"

i think dummit and foote will serve him for a while

[naive lava]

I heard that jacobson is pretty good

similar coveragen to lang

• cat theo

and actually describes something

[tender cobalt]

basic algebra or lectures in algebra one?

[naive lava]

basic algebra

the 2 volumes

first is an okay intro to algebra

[tender cobalt]

ye like something solid + self contained enough that i wont need a second course

[naive lava]

second has cat theo stuff

[naive lava]

why do you wanna learn algebra?

[tender cobalt]

group theory and galois theory sounds cool and will do algebraic geometry and algebraic number theory later

[tender cobalt]

okay let me check that one out

[heady ember]

Well, if nothing else, it is dummit thick

[tender cobalt]

well its really comprehensive..... it doesnt start galois theory until like page 500 😭

[tender cobalt]

@naive lava yo bro whats the difference between jacobson basic algebra I , vs hungerford or isaacs

[heady ember]

Is it comprehensive or does it just yap too much

[tender cobalt]

maybe it yaps too much

[naive lava]

hungerford will bore you

it's dry

[tender cobalt]

hungerford, isaacs, jacobsons go to galois theory after 200 pages

[naive lava]

if you wanna go for something dry

u can just try D&F or Lang

[heady ember]

It will fill your hunger for algebra with boredom

[naive lava]

D&F would have the advantage of being far more popular

and Lang is Lang

you can js tell ppl you used Lang for your first algebra course

immidiate infinite aura points

[tender cobalt]

This seems insane tho. 💀

But hey , same thickness as D&F and still goes to galois theory after like 250 pages

[naive lava]

it is

I tried it

[naive lava]

is it really 250 pages if each page has 5 theorems

[tender cobalt]

hows jacobson like

[tender cobalt]

☠️

[naive lava]

diluted lang

actually explains stuff

and cat theo

[tender cobalt]

what about isaacs

[naive lava]

if i wasn't gonna use aluffi i'd go for jacobson personally

[naive lava]

I haven't hear much about it

[tender cobalt]

ohhh hows aluffi btw

[naive lava]

prolly not the best for you

cos there's little to no commutative algebra

[tender cobalt]

😭

okay whats the verdict what i go for

Lang vs hungerford vs jacobson

[naive lava]

lang would be crazywork

hungerford is dry(nothing wrong with that tho)

[naive lava]

https://www.ocf.berkeley.edu/~abhishek/chicmath.htm#i:general-abstract-algebra

[tender cobalt]

Ok ill go for jacobson

[vital bane]

yo bro you gotta focus on Munkres🗿

[heady ember]

Basic

[tender cobalt]

😭munkres will move swiftly cuz of the study group i am in

I am plannign to study topology, algebra, linear algebra

three at once

so yeah 🐱

[heady ember]

Why

[tender cobalt]

want to get into algebraic geo and diff geo 👀

[heady ember]

Sure, but that doesn't mean you have to do all three simultaneously

[vital bane]

bad idea

take your time

don't rush

you will regret it

I speak from personal experience

go one at a time

[heady ember]

Says Nemesis, who has spent Ord years on Abbott

[vital bane]

Ord^Ord years

[heady ember]

Not well-defined

L

[vital bane]

simply define it🗿

[remote sparrow]

you don't even know whether you'll end up liking algebraic and differential geometry by the time you've studied all the subjects you mentioned

[tender cobalt]

i will like differential geometry FOR SURE

[heady ember]

You don't have to go one at a time. Just don't overload yourself and make sure you have your prerequisites.

[tender cobalt]

its cuz i dont got time 😭

next year i got my O levels

i wont be able to spend much time on math

[vital bane]

I don't see how that's a problem

[heady ember]

You don't even know what Ord is smh. Skill issue.

[tender cobalt]

whats Ord 🤔

[heady ember]

After O-Levels

[vital bane]

I'm pretty sure diff geo and alg geo aren't asked on O levels

[tender cobalt]

but whats gonna happen

[heady ember]

Based
Oh wait are you even replying to my msg

[vital bane]

after O levels ^

[tender cobalt]

ye it isnt

[tender cobalt]

true...

[remote sparrow]

it's fine if you have something at the end of the line to look forward to, but just take a moment to appreciate adjacent topics as you study

be open-minded

[tender cobalt]

okay well, so do i just study one subject at a time

[vital bane]

making 2% progress in 20 months and regreting that you didn't go one book at a time

[tender cobalt]

or two?

[vital bane]

start off with 1

then once you finish that book, increment by 1 if you want to

[tender cobalt]

okay..

[vital bane]

it's the class of all ordinal numbers

[tender cobalt]

20 MONTHS???

just 2% progress in 20 months? how did that happen man